Python move object on local axis
In order to make it faster you could also assign the values directly to the location property:

import bpy
import mathutils

# get the object
obj = bpy.data.objects["Object"]

# store the current location
loc = obj.location

# adjustment values
(x,y,z) = (1.0,2.0,3.0)

# adding adjustment values to the property
obj.location = loc + mathutils.Vector((x,y,z))


Assigning and adding the values in one line:

bpy.data.objects["Object"].location = bpy.data.objects['Object'].location + Vector((x,y,z))


Simple and fast is adding the adjustment values to each axis:

bpy.data.objects["Object"].location.x += 1.0
bpy.data.objects["Object"].location.y += 2.0
bpy.data.objects["Object"].location.z += 3.0